- 5.2 | Area
- 5.3 | Riemann Sums and Definite Integrals
- 5.4 | The Fundamental Theorem of Calculus
- 5.5 | Integration by Substitution

**Definition of Antiderivative**

A function \(F\) is an

**antiderivative**of \(f\) on an interval \(I\) when \(F'(x) = f(x)\) for all \(x\) in \(I\).

**Representation of Antiderivatives**

If \(F\) is an antiderivative of \(f\) on an interval \(I\), then \(G\) is an antiderivative of \(f\) on the interval \(I\) if and only if \(G\) is of the form \(G(x) = F(x) +C\), for all \(x\) in \(I\) where \(C\) is a constant.